Explaining the Level of Credit Spreads:

Transcription

1 Explaining the Level of Credit Spreads: Option-Implied Jump Risk Premia in a Firm Value Model Authors: M. Cremers, J. Driessen, P. Maenhout Discussant: Liuren Wu Baruch College Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 1/8

2 Overview of the paper Motivation: Several academic studies conclude that the observed credit spread is too wide (credit spread puzzle ) compared to historical default losses. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 2/8

3 Overview of the paper Motivation: Several academic studies conclude that the observed credit spread is too wide (credit spread puzzle ) compared to historical default losses. Specify a one-factor market model on firm values, Market risk and firm-specific risk are both modeled by jump-diffusions. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 2/8

4 Overview of the paper Motivation: Several academic studies conclude that the observed credit spread is too wide (credit spread puzzle ) compared to historical default losses. Specify a one-factor market model on firm values, Market risk and firm-specific risk are both modeled by jump-diffusions. Calibrate the model to Option prices on S&P 100 index and its constituents. Equity risk premium. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 2/8

5 Overview of the paper Motivation: Several academic studies conclude that the observed credit spread is too wide (credit spread puzzle ) compared to historical default losses. Specify a one-factor market model on firm values, Market risk and firm-specific risk are both modeled by jump-diffusions. Calibrate the model to Option prices on S&P 100 index and its constituents. Equity risk premium. Key findings: Incorporating jump risk premia (and calibrating them to options) is important to generate reasonable credit spreads. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 2/8

6 Ambitious work What they have done is daunting: Firm value process credit spread on corporate bond. Stock value as an option on firm value stock option as a compound option on firm value stock index as a portfolio of options on firm value stock index options as options on a portfolio of options on the firm value. The model is very detailed, with convoluted linkages. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 3/8

7 Ambitious work What they have done is daunting: Firm value process credit spread on corporate bond. Stock value as an option on firm value stock option as a compound option on firm value stock index as a portfolio of options on firm value stock index options as options on a portfolio of options on the firm value. The model is very detailed, with convoluted linkages. To make the calibration feasible, the model/calibration need to be highly stylized: Firm value dynamics are identical across different firms (same β). Static abstractions: constant volatility, constant arrival rate... Static calibrations using cross-sectional and time-series averages. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 3/8

8 Ambitious work What they have done is daunting: Firm value process credit spread on corporate bond. Stock value as an option on firm value stock option as a compound option on firm value stock index as a portfolio of options on firm value stock index options as options on a portfolio of options on the firm value. The model is very detailed, with convoluted linkages. To make the calibration feasible, the model/calibration need to be highly stylized: Firm value dynamics are identical across different firms (same β). Static abstractions: constant volatility, constant arrival rate... Static calibrations using cross-sectional and time-series averages. Give and take: To build a detailed model and make calibration possible, the model/calibration need to be highly stylized. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 3/8

9 Path to success Key claim of success: The paper can calibrate a structural model to generate reasonable credit spreads and hence solve the credit risk premium puzzle. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 4/8

10 Path to success Key claim of success: The paper can calibrate a structural model to generate reasonable credit spreads and hence solve the credit risk premium puzzle. Where there is risk, there is a risk premium puzzle. Stock market equity risk premium puzzle. Stock options market jump risk premium puzzle. Corporate bond market credit risk premium puzzle. Other markets: currency (forward risk premium), bond (term risk premium)... Different markets, same complaint: (1) too large, (2) strongly time varying. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 4/8

11 Path to success Key claim of success: The paper can calibrate a structural model to generate reasonable credit spreads and hence solve the credit risk premium puzzle. Where there is risk, there is a risk premium puzzle. Stock market equity risk premium puzzle. Stock options market jump risk premium puzzle. (Defaultable) bond market credit risk premium puzzle. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 4/8

12 Path to success Key claim of success: The paper can calibrate a structural model to generate reasonable credit spreads and hence solve the credit risk premium puzzle. Where there is risk, there is a risk premium puzzle. Stock market equity risk premium puzzle. Stock options market jump risk premium puzzle. (Defaultable) bond market credit risk premium puzzle. The risk premiums charged by stock (options) investors are consistent with the risk premiums charged by corporate bond investors. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 4/8

13 Path to success Key claim of success: The paper can calibrate a structural model to generate reasonable credit spreads and hence solve the credit risk premium puzzle. Where there is risk, there is a risk premium puzzle. Stock market equity risk premium puzzle. Stock options market jump risk premium puzzle. (Defaultable) bond market credit risk premium puzzle. The risk premiums charged by stock (options) investors are consistent with the risk premiums charged by corporate bond investors. Longstaff, Mithal, Neis: Credit spreads on corporate bonds are largely consistent with CDS. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 4/8

14 Path to success Key claim of success: The paper can calibrate a structural model to generate reasonable credit spreads and hence solve the credit risk premium puzzle. Where there is risk, there is a risk premium puzzle. Stock market equity risk premium puzzle. Stock options market jump risk premium puzzle. (Defaultable) bond market credit risk premium puzzle. The risk premiums charged by stock (options) investors are consistent with the risk premiums charged by corporate bond investors. Longstaff, Mithal, Neis: Credit spreads on corporate bonds are largely consistent with CDS. Investors in different financial markets are largely consistent with one another, but might be inconsistent with the academia... Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 4/8

15 Model design I agree with the conclusions: Incorporating jump risk (risk premia) is important to reconcile the difference between the statistical and risk-neutral distributions on stocks and stock indices. Structural models are useful in bring in the capital structure information to corporate bond valuation. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 5/8

16 Model design I agree with the conclusions: Incorporating jump risk (risk premia) is important to reconcile the difference between the statistical and risk-neutral distributions on stocks and stock indices. Structural models are useful in bring in the capital structure information to corporate bond valuation. Questions: What s the best way to model/calibrate jump risk and/or risk premium? What s the best way to incorporate capital structure information? Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 5/8

17 Model design I agree with the conclusions: Incorporating jump risk (risk premia) is important to reconcile the difference between the statistical and risk-neutral distributions on stocks and stock indices. Structural models are useful in bring in the capital structure information to corporate bond valuation. Questions: What s the best way to model/calibrate jump risk and/or risk premium? What s the best way to incorporate capital structure information? Can I simplify the model structure a bit to make the estimation more dynamic and less stylized? Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 5/8

18 Design questions If firms are identical, can we use a representative firm to arrive at the same conclusion? Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 6/8

19 Design questions If firms are identical, can we use a representative firm to arrive at the same conclusion? Is it possible to calibrate firm value dynamics to stock options (and other info) on one firm (without dragging in stock index options)? Index options are useful to identify the pricing of a market factor. Single-name options are probably enough to identify the risk/pricing on that specific company and hence reconcile the credit spread on the same firm. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 6/8

20 Design questions If firms are identical, can we use a representative firm to arrive at the same conclusion? Is it possible to calibrate firm value dynamics to stock options (and other info) on one firm (without dragging in stock index options)? Index options are useful to identify the pricing of a market factor. Single-name options are probably enough to identify the risk/pricing on that specific company and hence reconcile the credit spread on the same firm. What is causing what to jump? Firm value = equity value + debt value. Firm value jump stock price jump, credit spread jump. Stock price (market risk, perception of market risk) jump firm value jump, credit spread jump? (Perception of) credit risk jump stock price jump, firm value jump? Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 6/8

21 An alternative framework Stock price jumps to zero whenever default occurs. Stock option prices can be used to identify risk-neutral default intensity implications for out-of-sample bond pricing. It can be used to address similar questions: whether credit spread is consistent with stock option prices. Simplified linkage can accommodate more realistic dynamics: Both default arrival and return volatility can be stochastic. Leverage effect can be introduced through correlations between return and volatility. Pricing and model estimation are very simple and fast. Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 7/8

22 Bottom line I love what they are doing: Linking one market to another (and showing consistency) is a proven path to success in explaining risk premium puzzles: The risk premium might be puzzlingly large, but it is no more puzzling than the puzzle in the other market. I admire their ambition and effort: From firm value dynamics to stock index options involves many convoluted steps that need intelligence, patience, and hard work. For future research, a lot more can be done on building the linkages. There does not exist a dichotomy between structural models and reduced-form models. Where to start (firm, debt, equity) depends on the objective of the paper... Liuren Wu at 2006 European Finance Association meetings, August 23-26, 2006, Zurich, Switzerland Discussion: Explaining the Level of Credit Spreads - p. 8/8